The model-discriminating power of -to-e conversion Vincenzo - - PowerPoint PPT Presentation

The model-discriminating power of μ-to-e conversion

Vincenzo Cirigliano Los Alamos National Laboratory

Intensity Frontier Workshop, Argonne National Lab, April 25 2013

Charged LFV: general considerations

Extremely clean probe of BSM physics

νi γ

• ν oscillations imply that individual lepton family numbers are not

conserved (after all Le,μ,τ are “accidental” symmetries of SM)

• In SM + massive “active” ν, CLFV rates are tiny (GIM-suppression)

Petcov ’77, Marciano-Sanda ’77 ....

• Great “discovery” tools
• Observation near current limits ⇒ BSM physics
• Great “model-discriminating” tools
• Comparing μ →3e vs μ →eγ vs μ →e conversion (Z)

and μ →e vs τ→ μ vs τ→ e ⇒ learn about structure and flavor couplings of LBSM

Charged LFV: general considerations

In this talk I will discuss these points within an EFT framework (assumption: new physics originates at a high scale)

Effective theory framework

At low energy, BSM physics is described by local operators

Effective theory framework

• Dynamics described by an effective Lagrangian
• Key point: each model generates its unique pattern of operators /

couplings → distinctive signature in LE experiments

• LFV: probe strength of different operators and their flavor structure

• Several operators generated at dim6: rich phenomenology

Dominant in SUSY- GUT and SUSY see- saw scenarios Dominant in RPV SUSY

• Several operators generated at dim6: rich phenomenology

Dominant in SUSY- GUT and SUSY see- saw scenarios Dominant in RPV SUSY Dominant in RPV SUSY and RPC SUSY for large tan(β) and low mA

q q

• Several operators generated at dim6: rich phenomenology

Dominant in SUSY- GUT and SUSY see- saw scenarios Enhanced in triplet models, Left-Right symmetric models Dominant in RPV SUSY Z-penguin Dominant in RPV SUSY and RPC SUSY for large tan(β) and low mA

e e

δ++

...

q q

... + 4-lepton operators

• EFT framework: ask questions on LFV dynamics without choosing a

specific model (answers will help discriminating among models) ◆ What is the sensitivity to the effective scale Λ? What is the relative sensitivity of various processes? ◆ What is relative the strength of various operators (αD vs αS ... )? What experiments are needed to disentangle this? ◆ What is the flavor structure of the couplings ([αD]eμ vs [αD]τμ...)? How can we probe it? How does it relate to neutrino mixing?

in this talk

• EFT framework: ask questions on LFV dynamics without choosing a

specific model (answers will help discriminating among models) ◆ What is the sensitivity to the effective scale Λ? What is the relative sensitivity of various processes? ◆ What is relative the strength of various operators (αD vs αS ... )? What experiments are needed to disentangle this? ◆ What is the flavor structure of the couplings ([αD]eμ vs [αD]τμ...)? How can we probe it? How does it relate to neutrino mixing?

Observable CLFV @ 10-1? ⇔ new physics between weak and GUT scale

BRα→β ~ (vEW/Λ)4∗(αn)αβ2

• What combination of scale Λ + couplings produces observable rates?
• Current limit from μ →eγ implies

New physics at TeV scale (and reasonable mixing pattern) ⇒ LFV signals are within reach of planned searches

even after taking into account loop factors

Sensitivity to NP scale

Observable CLFV @ 10-1? ⇔ new physics between weak and GUT scale

BRα→β ~ (vEW/Λ)4∗(αn)αβ2

• What combination of scale Λ + couplings produces observable rates?
• Current limit from μ →eγ implies

Sensitivity to NP scale

• What about other processes? Relative sensitivity depends on the

model: each process probes a different combination of operators (related to model-discriminating question)

• A simple example with two
• perators

De Gouvea, Vogel 1303.4097

• κ controls relative strength of

dipole vs vector operator μ → eγ vs μ → 3e

dipole vector

• A simple example with two
• perators

De Gouvea, Vogel 1303.4097

• κ controls relative strength of

dipole vs vector operator μ → eγ vs μ → e conversion

dipole vector

• μ →eγ and μ →e conv. probe different combinations of operators
• By measuring the target dependence of μ→e conversion (and ratio to

μ→eγ BR) we can infer the relative strength of effective operators

x

Model-discriminating power

• How does this work? Conversion amplitude has non-trivial dependence
• n target nucleus, that distinguishes D,S,V underlying operators

Czarnecki-Marciano- Melnikov Kitano-Koike-Okada

• How does this work? Conversion amplitude has non-trivial dependence
• n target nucleus, that distinguishes D,S,V underlying operators

Czarnecki-Marciano- Melnikov Kitano-Koike-Okada

• Lepton wave-functions in EM field

generated by nucleus

• Relativistic components of muon wave-

function give different contributions to D,S,V overlap integrals. For example:

• Expect largest discrimination for heavy

target nuclei

• How does this work? Conversion amplitude has non-trivial dependence
• n target nucleus, that distinguishes D,S,V underlying operators

Czarnecki-Marciano- Melnikov Kitano-Koike-Okada

• Lepton wave-functions in EM field

generated by nucleus

• Relativistic components of muon wave-

function give different contributions to D,S,V overlap integrals. For example:

• Expect largest discrimination for heavy

target nuclei

• Sensitive to hadronic and nuclear properties

• Dominant sources of uncertainty:
• Scalar matrix elements
• Neutron density (heavy nuclei)

∈ [0, 0.4] → [0, 0.05]

JLQCD 2008

[0.04, 0.12]

ChPT Lattice range 2012 (Kronfeld 1203.1204)

→ 53 +21-10 MeV (45 ±15) MeV

Test hypothesis of single-operator dominance

• One unknown parameter ([αD,V,S]eμ /Λ2) → predict ratios of LFV BRs

D

B(µ → e,Z) B(µ → eγ)

D,V,S B(µ → e,Z2) B(µ → e,Z1)

dipole vector scalar

• If μ →eγ and μ →e conversion are observed, can test dipole model
• In principle, any single-operator dominance model can be tested with

two μ→e conversion rates (even if μ→eγ is not observed)

• Test dipole-dominance model with μ→eγ and one μ→e rate

Kitano-Koike-Okada ‘02 VC-Kitano-Okada-Tuzon ‘09

B(µ → e,Z) B(µ → eγ)

O(α/π)

Z

Pattern: 1) Behavior of overlap integrals** 2) Total capture rate (sensitive to nuclear structure) 3) Deviations would indicate presence of scalar / vector terms

→ free outgoing electron wf (average value)

** Qualitative behavior of overlap integrals

Kitano-Koike-Okada

• Test any single-operator model via target-dependence of μ→e rate
• Essentially free of theory uncertainty (largely cancels in ratios)
• Discrimination: need ~5% measure of Ti/Al or ~20% measure of Pb/Al
• Ideal world: use Al and a large Z-target (D,V,S have largest separation):

challenge for experiments

VC-Kitano-Okada-Tuzon 2009

Al Ti Pb

Z

D S V(γ) V(Z)

• Z couples predominantly to

neutrons

• γ couples to protons

1 2 3 4

• Unknown parameters: [α1]eμ /Λ2 , [α2]eμ /Λ2
• Hypothesis can be tested with two double ratios (three LFV

measurements!!). For example:

• If “single-operator” dominance hypothesis fails, consider next

simplest case: two-operator dominance (DV, DS, SV)

Test “two-operator” models

B(µ → e,Al) B(µ → eγ)

DV, DS SV

B(µ → e,Pb) B(µ → e,Al)

B(µ → e,Ti) B(µ → e,Al)

B(µ → e,Pb) B(µ → e,Al)

Relative sign: +

VC-Kitano-Okada-Tuzon 2009

• Consider

V and D

dipole vector dipole vector Relative sign: - αV αV

• Consider S and D: realized in SUSY via competition between dipole

and scalar operator (mediated by Higgs exchange)

dipole scalar

• Uncertainty from strange form factor largely reduced by lattice QCD

thin error band → realistic discrimination ∈ [0, 0.4] → [0, 0.05]

JLQCD 2008

fat error band Relative sign: +

VC-Kitano-Okada-Tuzon 2009

dipole scalar Relative sign: -

• Consider S and D: realized in SUSY via competition between dipole

and scalar operator (mediated by Higgs exchange)

• Uncertainty from strange form factor largely reduced by lattice QCD

thin error band → realistic discrimination ∈ [0, 0.4] → [0, 0.05]

JLQCD 2008

fat error band

VC-Kitano-Okada-Tuzon 2009

dipole scalar Relative sign: -

• Consider S and D: realized in SUSY via competition between dipole

and scalar operator (mediated by Higgs exchange)

• Uncertainty from strange form factor largely reduced by lattice QCD

thin error band → realistic discrimination ∈ [0, 0.4] → [0, 0.05]

JLQCD 2008

fat error band

In summary:

• Theoretical hadronic uncertainties under control (OK for 1-operator

dominance, need Lattice QCD for 2-operator models)

• Realistic model discrimination requires measuring Ti/Al at <5% or

Pb/Al at <20%

• In principle, can perform similar analysis for hadronic vs radiative tau

decays at next generation B factory

Explicit realization: SUSY see-saw scenario

• See-saw scenario: mixing in L-slepton mass matrices
• Dipole vs scalar operator, mediated by Higgs exchange

Kitano-Koike-Komine-Okada 2003

/mA2 /mSL2

Explicit realization: SUSY see-saw scenario

• See-saw scenario: mixing in L-slepton mass matrices
• Dipole vs scalar operator, mediated by Higgs exchange
• Learn about SUSY parameters

VC-Kitano-Okada-Tuzon 2009

Conclusions

• Charged LFV: deep probes of physics BSM
• “Discovery” tools: clean, high scale reach (beyond LHC)
• “Model-discriminating” tools
• Observation of more than one mode → diagnosing power:
• Relative strength of operators through μ →eγ vs μ →e

conversion in different nuclei [hadronic uncertainty OK]

• Structure of flavor breaking sources through μ vs τ LFV BRs

( )

Extra Slides

Definition of models: D, S, V(Z), V(γ)

Vector model: V(γ) Vector model: V(Z) Dipole model Scalar model

• Details on the uncertainties

• Experimental status (90% CL): muons

10-/14 (MEG at PSI) 10-16/17 → -18 (Mu2e, COMET)

• μ-to-e conversion rate

(normalized to total muon capture rate)

10-14/16 (PSI or MuSIC?)

• Experimental status: taus (90% BR limits from PDG)

...

10-9 sensitivities at future super-B factory (KEK)